# Consider the mapping f : R2 -> R2 given by f(x, y) = (x2 – y’, 2xy). (a) Compute the Jacobian matrix of f at P = (4, -7), i.e. Df(P). (b) Show that the Jacobian matrix found in part (a), when view a linear transfor- mation of R’ to itself, preserves angles between vectors, i.e.

Consider the mapping f : R2 -> R2 given by f(x, y) = (x2 – y’, 2xy).

(a) Compute the Jacobian matrix of f at P = (4, -7), i.e. Df(P).

(b) Show that the Jacobian matrix found in part (a), when view a linear transfor-

mation of R’ to itself, preserves angles between vectors, i.e.

(Df(P)u) .(Df(P) v)

1-V

I Df(P)u|| DS(P)v|

(c) Show that this property of the Jacobian matrix of f holds for all point P on the

plane not just P = (4, -7). Remark: f is called a conformal transformation.

Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code “Newclient”

The post Consider the mapping f : R2 -> R2 given by f(x, y) = (x2 – y’, 2xy). (a) Compute the Jacobian matrix of f at P = (4, -7), i.e. Df(P). (b) Show that the Jacobian matrix found in part (a), when view a linear transfor- mation of R’ to itself, preserves angles between vectors, i.e. appeared first on Superb Professors.